16 March 2008

The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Eugene Wigner's famous essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences is available online.

6 comments:

Glenn said...

Thank you for posting that link! Great article, and it needs to be read by a very wide audience.

CarlBrannen said...

The basic problem with the use of mathematics in physics is precisely its unreasonable effectiveness. If you have enough parameters, you can fit a curve, but that really doesn't tell you anything about the underlying reality.

And the historical fact is that as soon as one curve is shown to fit, all other curves are ignored until that first curve is disproven by later experiment. But even "disproven" is interpreted quite favorably in the direction of the first curve fit. So when symmetry clearly fails, physicists talk about symmetry breaking.

The other problem with the use of mathematics is the belief that if a theory is beautiful, and it fits the data, then it must be a part of reality. The problem is that there is a great deal of mathematics and all of it is beautiful. So the tendency is to randomly walk the parameter space of mathematics until one finds a curve that fits, and then that theory crowds out all other possibilities. And when cracks appear in it, they are are fixed by epicycles, circles on circles.

The attraction of a good curve fit is so overwhelming that even if the theory behind the curve implies ridiculous theories of reality, the result is not that physicists look for a version of mathematics that gives the same curve fit but without the silly implications, but instead they almost universally talk about how strange nature is. It's science fiction instead of science.

Anonymous said...

I wonder what you think of Eric Raymond's essay "The Utility of Mathematics" (http://catb.org/~esr/writings/utility-of-math/)
which can be read as a reply. I think Raymond does a pretty good job of offering a response.

Anonymous said...

It was rather interesting for me to read that article. Thanx for it. I like such themes and anything that is connected to this matter. I definitely want to read a bit more soon.

Anonymous said...

It is certainly interesting for me to read the article. Thanx for it. I like such topics and anything that is connected to them. I definitely want to read a bit more soon.

Anonymous said...

Keep on posting such articles. I love to read blogs like this. By the way add more pics :)